CN108932306A - It is a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed - Google Patents
It is a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed Download PDFInfo
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Abstract
The present invention discloses a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed, it uses the model of constraint satisfaction problemx CSP, the model of the constraint satisfaction problemx of the information architectures Subgraph Isomorphism problem such as the node of analytical model figure and target figure, side first, addition destroys symmetry constraint, further according to the method for solving of constraint satisfaction problemx, the model established is solved.Non-symmetric technique is destroyed to include detection automorphism node and destroy two steps of constraint by the way that the generation of Schreier-Sims algorithm is symmetrical.Due to symmetrically destroying technology for solving the symmetry in CSP, the operation of permutation group is generated by mono- simms algorithm of Shi Laiaier and destroys symmetry constraint, can be avoided the binary search of symmetrical subtree, reduces combinatorial complexity.Therefore in algorithm implementation procedure, search space is effectively reduced, the solution efficiency of problem is improved, there is good practicability.
Description
Technical field
The present invention relates to diagram data constraint solving technical fields, and in particular to it is a kind of based on the Subgraph Isomorphism symmetrically destroyed about
Beam method for solving.
Background technique
With the arrival of big data era, the massive multi-source data in internet and life are just with unprecedented
Speed generate and accumulate, there is close relevances between these data, how it are effectively analyzed and be excavated
It is the severe challenge and important opportunity that academic circles at present faces.Scheme as the basic structure for indicating relationship between data, in many
The problem of field extensive application, many problems in life can be converted into one based on figure, and using on figure
Correlation theory and algorithm are solved.Wherein, graph pattern matching technology is to realize the important means efficiently inquired on diagram data,
The fields such as biological information, social networks have important application value.
In practical problem, efficient, accurate matching inquiry is carried out to diagram data and still suffers from many problems, is especially existed
It is still to be improved on time complexity and space complexity.For effective solution figure matching problem, Many researchers are used
The basic thought of constraint satisfaction problemx (Constraint Satisfaction Problem, CSP) is straight by figure matching problem
Switch through the model for turning to a constraint satisfaction problemx, solution figure matching problem is reached by analysis to CSP model and solution
Purpose.A general solution of the constraint satisfaction problemx as the large amount of complex problem in artificial intelligence and computer science
Example, it is therefore an objective to find meet constrained each variable one or more assignment.So far, to the research of CSP algorithm
Very extensively and profoundly, and there are many more mature efficient algorithms, but since constraint satisfaction problemx is usually all np hard problem, so
It will be inevitably by the restriction of combinatorial complexity in solution procedure.When Subgraph Isomorphism is portrayed as CSP model, due to
The design feature of figure determines that it includes a large amount of symmetrical structures, and these symmetrical structures will cause symmetrical subtree in the search,
In solution procedure, if current matching success, then all symmetrical subtrees are still to enumerate, in the solution finally acquired, it will produce
The different variants of raw a large amount of same solutions, waste time and space in this way.
Summary of the invention
The present invention is directed to the process of existing Subgraph Isomorphism problem solving inevitably by the restriction of combinatorial complexity
Problem provides a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed.
To solve the above problems, the present invention is achieved by the following technical solutions：
It is a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed, specifically include that steps are as follows：
The automorphism nodal test of step 1, ideograph, i.e.,：
The top partition node of ideograph and lower partition node are respectively divided into different by step 1.1, the degree by node
In unit, the identical node division of moderate is same unit；The unit number of the unit number and lower partition of top partition at this time
It is n, there is the top partition unit of mutually unison node and corresponding lower partition unit label having the same；I ∈ 1,
2 ..., n；
Step 1.2, as top partition unit AiWhen interior number of nodes is greater than 1, by top partition unit AiInterior each section
Point successively with corresponding lower partition unit BiInterior all nodes are combined pairing, and judge that the node of every group of pairing is one by one
It is no to belong to same mapping set：
If the node currently matched belongs to same mapping set, a set of paired node judges under；
Otherwise, it in the node currently matched, will belong to originally in top partition unit A respectivelyiNode be put into newly-built upper layer
Zoning unit An+iIn, it belongs to originally in lower partition unit BiNode be put into newly-built lower partition unit Bn+iIn；
Step 1.3, the top partition unit A for creatingn+iWith newly-built lower partition unit Bn+iInterior node, observation
Its abutment points marks neibor for these abutment points addition connection side, and records newly-built top partition unit An+iThe neighbour of interior nodes
Contact said units label；
The corresponding top partition unit A of step 1.4, the said units label to each abutment pointsiWith lower partition list
First BiInterior node is classified：
For top partition unit AiInterior node：There to be the node of connection side mark neibor label to be retained in the upper layer point
Area unit AiIt is interior, the node of no connection side mark neibor label is moved into newly-built top partition unit from former said units
A2n+iIn, while recording this newly-built top partition unit A2n+iUnit mark and be stored in temporary marker set Nlabel；
For lower partition unit BiInterior node：There to be the node of connection side mark neibor label to be retained in the lower layer point
Area's unit BiIt is interior, the node of no connection side mark neibor label is moved into newly-built lower partition unit from former said units
B2n+iIn；
Step 1.5 successively chooses top partition unit AiWith corresponding lower partition unit Bi：If top partition unit Ai
With lower partition unit BiInterior number of nodes is inconsistent, then goes to step 1.2；Otherwise, step 1.6 is gone to；
Step 1.6 takes the unit in temporary marker set Nlabel to mark, and finds upper layer corresponding with this element label point
Area unit Ai, and observe top partition unit AiThe abutment points of interior nodes mark neibor for these abutment points addition connection side,
And record this top partition unit AiThe abutment points said units of interior nodes mark, and go to step 1.4；
Step 1.7, when top partition and each unit of lower partition only include a node, if in top partition
Node a it is identical as the said units label of node b in lower partition, and in the node b in top partition and lower partition
Node a said units label it is identical, then node a and node b is one group of automorphism node, and every group of automorphism node forms one
A mapping set；
Step 2, after the completion of all automorphism nodal tests of ideograph, obtain a series of displacements, these displacement constitute
Permutation group operates permutation group by mono- simms algorithm of Shi Laiaier, i.e., obtains stablizing chain by permutation group first,
Secondary utilization stablizes chain and acquires coset, finally, generating the constraint relationship between node using coset；
Step 3, using the constraint relationship of the obtained ideograph interior joint of step 2, in conjunction with the universal constraining of Subgraph Isomorphism,
The symmetrical destruction CSP model for constructing Subgraph Isomorphism problem solves this symmetrical CSP model that destroys, target figure can be obtained
In the subgraph with the mode isomorphism of graph, and these solution mutually not be symmetric solution.
The present invention discloses a kind of Subgraph Isomorphism constraint solving method based on destruction non-symmetric technique, and constraint satisfaction is used to ask
Inscribe the model of (CSP), the first constraint satisfaction of the information architectures Subgraph Isomorphism problem such as the node of analytical model figure and target figure, side
The model of problem, addition destroy symmetry constraint and ask further according to the method for solving of constraint satisfaction problemx the model established
Solution.Destroying non-symmetric technique includes detecting automorphism node and by the life of mono- simms of Shi Laiaier (Schreier-Sims) algorithm
Two steps are constrained at symmetrical destroy.Due to symmetrically destroying technology for solving the symmetry in CSP, pass through mono- simms of Shi Laiaier
Algorithm generates the operation of permutation group and destroys symmetry constraint, can be avoided the binary search of symmetrical subtree, reduces combinatorial complexity.
Therefore in algorithm implementation procedure, search space is effectively reduced, the solution efficiency of problem is improved, there is good practicability.
Compared with prior art, the present invention is using destruction non-symmetric technique, and provides new automorphism nodal test method.?
Solve Subgraph Isomorphism during, using destroy symmetry constraint destroy symmetric solution, retain unique solution, thus alleviate Subgraph Isomorphism into
The process that row solves inevitably restriction by combinatorial complexity the problem of.
Detailed description of the invention
Fig. 1 is the given example figure of the preferred embodiment of the present invention, wherein (a) is ideograph, it (b) is target figure.
Fig. 2 is automorphism nodal test process, and wherein Circled numbers indicate detection ordering.
Fig. 3 is Subgraph Isomorphism solution procedure.
Fig. 4 is the flow chart of the constraint solving of Subgraph Isomorphism problem.
Specific embodiment
Below by taking the comparison problem of anti-AIDS compound as an example, the present invention is described in more detail.
Fig. 1 (a) and Fig. 1 (b) is respectively the given ideograph and target figure of the present embodiment.The present embodiment considers two figures
Between corresponding the constraint relationship, establish constraint satisfaction problemx model and solved, i.e., based on the symmetrical Subgraph Isomorphism for destroying technology
Constraint solving method.This method includes：The automorphism point of checking mode figure, by mono- simms algorithm of Shi Laiaier to permutation group
Operation, which generates, destroys symmetry constraint, and establishing CSP model using the constraint relationship destroyed in symmetry constraint and graph structure, (including degree is about
Beam, side constraint), it is finally completed Subgraph Isomorphism CSP model solution.Since the present invention considers the problems of symmetric solution in Subgraph Isomorphism,
The problem of establishing corresponding constraint and destroy symmetric solution, therefore assembled state Space Explosion in Subgraph Isomorphism solution can be effectively relieved.
The detection of step 1 automorphism.
The top partition π for detecting initial slave pattern figure of step 11, automorphism nodea={ A1|A2|…|AnAnd lower layer point
Area πb={ B1|B2|…|BnTwo subregions start, wherein AiIndicate the unit of top partition, BiIndicate the unit of lower partition,
Wherein i=1,2 ..., n.Node in each unit has identical and other units connection relationships.Due to all nodes
Spend identical, therefore initial πaAnd πbFor all nodes respectively in 1 unit, this two unit labels are all 1.As shown in Figure 1, u1,
U2, u3, u4 use 1,2,3,4 expressions, π respectivelya={ 1,2,3,4 }, πb={ 1,2,3,4 }.
If step 12, πaActive cell AiInterior number of nodes is greater than 1, by πaActive cell AiInterior node is successively
With πbActive cell BiInterior node pairing chooses B if the node of pairing belongs to same mapping setiNext section
Point, otherwise, by the A of pairingjWith BjInterior node is correspondingly placed into newly-built unit.As shown in Fig. 2 1., πaInterior joint 1 and πbMiddle section
1 pairing of point, is placed in πaWith πbIn in new separate unit, this 2 units are labeled as 2.
Step 13, the new unit interior nodes of analysis, observe its abutment points, for these abutment points addition connection side label
Neibor, and record abutment points said units label.As shown in Fig. 2 2., πaIn node 1 abutment points be node 2 and 3,
Come under the unit labeled as 1.Neibor label is added for node 2 and 3.πbThe abutment points of interior joint 1 are node 2 and 3, for section
The addition neibor label of point 2 and 3.
Step 14, by obtained by step 13, πaUnit involved in 1 abutment points of interior joint is Unit 1, and Unit 1 includes node
2,3,4, interior joint 2 and 3 has neibor label, therefore is retained in former unit, and node 4 is marked without neibor, therefore will section
Point 4 moves into newly-built unit from former unit, this newly-built unit is labeled as 3.Label 3 is added into Nlabel set.πbInterior joint 1 is adjacent
Unit involved in contact is Unit 1, and interior joint 2 and 3 has neibor label, therefore is retained in former unit, and 4 nothing of node
Neibor label, therefore node 4 is moved into newly-built unit from former unit, this newly-built unit is labeled as 3.
Step 15 successively chooses πaInterior unit AiAnd its corresponding lower unit BiIf AiWith BiInterior number of nodes
Inconsistent, current pairing failure, algorithm dates back step 1.2.In this example, label is 2,3 unit internal segment in top partition
Point is consistent for the number of nodes in Unit 1,2,3 with respective markers in lower partition；
Step 16 successively takes unit in Nlabel to mark, and finds π corresponding with this labelaInterior unit, repeat step 13 to
15；
Step 17, when each unit of top partition and lower partition only includes a node, if πaIn node a with
πbIn node b said units label it is identical, and πaIn node b and πbIn node a said units label it is identical, obtain
To automorphism node a and b.Automorphism node constitutes displacement, the operation for subsequent permutation group.As shown in Fig. 2 3., πaMiddle section
Point 2 and πbAfter interior joint 3 matches, unit obtains π by analysisbInterior joint 2 and πa3 said units of interior joint label is identical, therefore
To one group of automorphism node (2,3), i.e., a displacement [1,3,2,4] is obtained with original image automorphism after the exchange of node 2 and 3.Such as figure
In 2 5. shown in, obtain two groups of automorphism nodes (1,2), the exchange of (3,4), i.e. node 1 and 2 after node 3 and 4 exchanges simultaneously with original
Realization obtains a displacement [2, Isosorbide-5-Nitrae, 3].
Step 18, in the detection process, mapping set for store the node that can mutually map, by 3. obtain P1=2,
3 }, therefore node 2 and 3 mutually maps, and obtains mapping set { 1 }, { 2,3 }, { 4 }.By 5. obtaining, P2={ 1,2 } { 3,4 }, and because
For P1={ 2,3 }, 1,2,3,4 can mutually map known to transitivity, and updating mapping set is { 1,2,3,4 }.
Step 2, which is generated, destroys symmetry constraint.
Step 21 is replaced according to the automorphism node that detection obtains, and a series of displacements constitute permutation group, permutation group G
In displacement by the way that different location of the node switching into sequence is acted on sequence node.But some displacements will not change
All nodes, and some nodes are left in original position, this kind of displacement is referred to as stabilizer, stabilizer, which is constituted, stablizes chain
G1, G1..., Gn, in this example, obtain G0=G={ [1,2,3,4], [1,3,2,4], [2, Isosorbide-5-Nitrae, 3] }, wherein [1,2,3,4] is i.e.
For original graph.
G1It indicates in G, the displacement for remaining unchanged node 1 obtains：
G1={ [1,2,3,4], [1,3,2,4] }
G2It indicates in G1In, the displacement for remaining unchanged node 2 obtains：
G2={ [1,2,3,4] }
It can similarly obtain：
G3={ [1,2,3,4] }
G4={ [1,2,3,4] }
Step 22, according to stablize chain obtain coset, coset UiIt indicates in Gi-1In, the set of the value of node i mapping.
U1It indicates in G0In, the node set that node 1 maps obtains：
U1={ 1,2 }
U2It indicates in G1In, the node set that node 2 maps obtains：
U2={ 2,3 }
It can similarly obtain：
U3={ 3 }
U4={ 4 }
Step 23 enables InIndicate that one includes 1 to n set of integers, gives j ∈ In, r (j) expression can make j ∈ UiMaximum
I, if being allowed to meet without such Ui other than Uj, r (j)=j.It can thus be concluded that：
R (1)=1, r (2)=1, r (3)=2, r (4)=4
According to the r (j) acquired, the destruction symmetry constraint for acting on target node of graph number is obtained, this constraint specification is as follows：
In this example, destroying symmetry constraint is specially：
NUM1< NUM2, NUM2< NUM3
In the matching process, the number of target node of graph corresponding to mode node 1 is less than mode node 2 to this constraint representation
Corresponding target such as node serial number, the number of target node of graph corresponding to mode node 2 are less than the corresponding target of mode node 3
Such as node serial number.
The CSP model of step 3 Subgraph Isomorphism problem.
Step 31 analyzes the constraint informations such as given two figure interior joints, sides, establishes the CSP of Subgraph Isomorphism problem
Model.For given two figures, respectively ideograph Gp=(Vp, Ep) and target figure Gt=(Vt, Et), wherein VpAnd VtTable respectively
Show the set of two figure interior joints, EpAnd EtRespectively indicate the set on side in two figures.The information such as analysis chart interior joint, side use
Subgraph Isomorphism problem is described as a constraint satisfaction problemx, and establishes Subgraph Isomorphism and ask by the basic thought of constraint satisfaction problemx
The CSP model of topic defines a triple CSP P<V, D, C>：I.e.
(1) variables set V：Variable x corresponding to any vertex u in ideographuMeet：X={ xu|u∈V}；
(2) codomain D：Aleatory variable xuCodomain meet：
(3) the constraint relationship collection C={ C1, C2, C3, C4}；
The target that CSP is solved is to find some or all instantiations, so that for all variables of variables set X, assignment
All meet corresponding constraint.Example modeling as shown in Figure 1, wherein scope of a variable X includes node u1, u2, u3, u4, uses x1 respectively,
X2, x3, x4 are indicated.Initial each variable codomain is v1, v2, v3, and v4, v5 are indicated with number 1,2,3,4,5,6 respectively.
Step 32, C1Degree of a representation constraint, i.e. Deg (u)≤Deg (u '), degree of vertex is not in the constraint requirements ideograph
Greater than degree of vertex in target figure, the constraint is for reducing initial codomain.In this example, by target node of graph 6 from each initial value
Delete to obtain D (x1)={ 1,2,3,4,5 } in domain, D (x2)={ 1,2,3,4,5 }, D (x3)={ 1,2,3,4,5 }, D (x4)=1,
2,3,4,5 }.
Step 33 determines variable match according to the size of degree sequentially, and in this example, ideograph node degree is identical, therefore
Sequence ligand is random.According to x1 in this example, the sequence of x2, x3, x4 are successively solved.According to matching order, if a Candidate Set, initially
Changing Candidate Set is " Ф ", according to variable instanceization sequence, is successively instantiated to the node variable in datagram, is become from initial
It selects a variable to be instantiated in quantity set, and in instantiation process, judges whether to meet corresponding constraint condition C2、C3、
C4、C5.If conditions are not met, then tracing back to first, there are the nodes of the constraint relationship with current Evaluation node, and are assigned again to it
Value repeats above step, continues to instantiate.
Step 34, C2For complete different constraint, indicate each of constraint satisfaction problemx variable in respective codomain
At least there is a value, and the value of each variable is different.This constraint specification is as follows, to variable x1, x2 ..., xn
As shown in figure 3, that will delete value 1 from variable x2, the codomain of x3, x4 after value 1 is assigned to variable x1, it equally, will
After value 2 is assigned to variable x2, value 2 is deleted from variable x3, the codomain of x4.
Step 35, C3It is constrained for side, the abutment points in intermediate scheme figure, corresponding target node of graph is also abutment points.This
Constraint specification is as follows, arbitrary node u, v ∈ Gp(u < v), has：
Wherein edge (Gp, u, v) and it indicates in ideograph, node u and v are abutment points.As shown in Fig. 3 1., work as variable
When x4 value 5, mode node corresponding to variable x4 is the abutment points of the corresponding mode node of variable x3, and 5 corresponding targets
The abutment points of the corresponding destination node of node non-3, therefore this time instantiation is not required Subgraph Isomorphism solution completely, in Fig. 3 institute
In the search tree shown, have × search branch be all be unsatisfactory for side constraint search.
Step 36, C4For destruction symmetry constraint, known by step 33, in this example, target figure section corresponding to mode node 1
Point number is less than 2 corresponding target such as node serial number of mode node, and the number of target node of graph corresponding to mode node 2 wants small
In 3 corresponding target such as node serial number of mode node.In solution procedure, for deleting the assignment for being unsatisfactory for this constraint.Such as Fig. 3
Shown, the search branching representation of figure acceptance of the bid stain is unsatisfactory for this constraint.
The method for solving (flow chart is as shown in Figure 4) of Subgraph Isomorphism problem is obtained by above method, finally acquires satisfaction
The example of constraint is：
{ x1=1, x2=2, x3=3, x4=4 } and { x1=1, x2=2, x3=4, x4=5 }
This implementation uses the model of constraint satisfaction problemx (CSP), passes through automorphism detection and mono- Lyceum of Shi Laiaier first
This algorithm generates symmetrical destroy and constrains, secondly the information such as node, side of analytical model figure and target figure, destroys about in conjunction with symmetrical
Beam constructs the model of the constraint satisfaction problemx of Subgraph Isomorphism problem, finally according to the method for solving of constraint satisfaction problemx, to being built
Vertical model is solved, and solution technique is applied in anti-AIDS compound comparison.Analysis is extracted in compound
Information, figure interior joint corresponding element, side correspond to chemical bond, construct anti-AIDS compound comparison chart.In algorithm implementation procedure, effectively
Search space is reduced, the solution efficiency of problem is improved, there is good practicability.
It should be noted that although the above embodiment of the present invention be it is illustrative, this be not be to the present invention
Limitation, therefore the invention is not limited in above-mentioned specific embodiment.Without departing from the principles of the present invention, all
The other embodiment that those skilled in the art obtain under the inspiration of the present invention is accordingly to be regarded as within protection of the invention.
Claims (1)
1. a kind of based on the Subgraph Isomorphism constraint solving method symmetrically destroyed, characterized in that specifically include that steps are as follows：
The automorphism nodal test of step 1, ideograph, i.e.,：
The top partition node of ideograph and lower partition node are respectively divided into different units by step 1.1, the degree by node
In, the identical node division of moderate is same unit；The unit number of top partition and the unit number of lower partition are at this time
N has the top partition unit of mutually unison node and corresponding lower partition unit label having the same；
Step 1.2, as top partition unit AiWhen interior number of nodes is greater than 1, by top partition unit AiInterior each node according to
It is secondary with corresponding lower partition unit BiInterior all nodes are combined pairing, and judge whether the node of every group of pairing belongs to one by one
In same mapping set：
If the node currently matched belongs to same mapping set, a set of paired node judges under；
Otherwise, it in the node currently matched, will belong to originally in top partition unit A respectivelyiNode be put into newly-built top partition list
First An+iIn, it belongs to originally in lower partition unit BiNode be put into newly-built lower partition unit Bn+iIn；
Step 1.3, the top partition unit A for creatingn+iWith newly-built lower partition unit Bn+iInterior node observes its neighbour
Contact marks neibor for these abutment points addition connection side, and records newly-built top partition unit An+iThe abutment points of interior nodes
Said units label；
The corresponding top partition unit A of step 1.4, the said units label to each abutment pointsiWith lower partition unit BiIt is interior
Node classify：
For top partition unit AiInterior node：There to be the node of connection side mark neibor label to be retained in the top partition list
First AiIt is interior, the node of no connection side mark neibor label is moved into newly-built top partition unit A from former said units2n+i
In, while recording this newly-built top partition unit A2n+iUnit mark and be stored in temporary marker set Nlabel；
For lower partition unit BiInterior node：There to be the node of connection side mark neibor label to be retained in the lower partition list
First BiIt is interior, the node of no connection side mark neibor label is moved into newly-built lower partition unit B from former said units2n+i
In；
Step 1.5 successively chooses top partition unit AiWith corresponding lower partition unit Bi：If top partition unit AiWith under
Layer zoning unit BiInterior number of nodes is inconsistent, then goes to step 1.2；Otherwise, step 1.6 is gone to；
Step 1.6 takes the unit in temporary marker set Nlabel to mark, and finds top partition list corresponding with this element label
First Ai, and observe top partition unit AiThe abutment points of interior nodes mark neibor for these abutment points addition connection side, and remember
Record this top partition unit AiThe abutment points said units of interior nodes mark, and go to step 1.4；
Step 1.7, when top partition and each unit of lower partition only include a node, if the section in top partition
Point a is identical as the said units label of node b in lower partition, and the node b in top partition and the section in lower partition
The said units label of point a is identical, then node a and node b is one group of automorphism node, and every group of automorphism node forms one and reflect
Penetrate set；
Step 2, after the completion of all automorphism nodal tests of ideograph, obtain a series of displacements, these displacement constitute displacement
Group, operates permutation group by mono- simms algorithm of Shi Laiaier, i.e., obtains stablizing chain by permutation group first, secondly benefit
Coset is acquired with chain is stablized, finally, generating the constraint relationship between node using coset；
Step 3 is constructed using the constraint relationship of the obtained ideograph interior joint of step 2 in conjunction with the universal constraining of Subgraph Isomorphism
The symmetrical destruction CSP model of Subgraph Isomorphism problem solves this symmetrical CSP model that destroys, can be obtained in target figure
With the subgraph of the mode isomorphism of graph, and these solution mutually not be symmetric solution；
Above-mentioned i ∈ 1,2 ..., n.
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| CN116610896A (en) * | 2023-07-07 | 2023-08-18 | 浙江大学高端装备研究院 | Manufacturing service supply and demand matching method based on subgraph isomorphism |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022041023A1 (en) * | 2020-08-27 | 2022-03-03 | 清华大学 | Sub-graph matching policy determination method, sub-graph matching method, sub-graph counting method and calculation device |
| CN116610896A (en) * | 2023-07-07 | 2023-08-18 | 浙江大学高端装备研究院 | Manufacturing service supply and demand matching method based on subgraph isomorphism |
| CN116610896B (en) * | 2023-07-07 | 2023-10-27 | 浙江大学高端装备研究院 | Manufacturing service supply and demand matching method based on subgraph isomorphism |
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